Dealing with missing standard deviation and mean values in meta-analysis of continuous outcomes: a systematic review

Background: Rigorous, informative meta-analyses rely on availability of appropriate summary statistics or individual participant data. For continuous outcomes, especially those with naturally skewed distributions, summary information on the mean or variability often goes unreported. While full reporting of original trial data is the ideal, we sought to identify methods for handling unreported mean or variability summary statistics in meta-analysis. Methods: We undertook two systematic literature reviews to identify methodological approaches used to deal with missing mean or variability summary statistics. Five electronic databases were searched, in addition to the Cochrane Colloquium abstract books and the Cochrane Statistics Methods Group mailing list archive. We also conducted cited reference searching and emailed topic experts to identify recent methodological developments. Details recorded included the description of the method, the information required to implement the method, any underlying assumptions and whether the method could be readily applied in standard statistical software. We provided a summary description of the methods identified, illustrating selected methods in example meta-analysis scenarios. Results: For missing standard deviations (SDs), following screening of 503 articles, fifteen methods were identified in addition to those reported in a previous review. These included Bayesian hierarchical modelling at the meta-analysis level; summary statistic level imputation based on observed SD values from other trials in the meta-analysis; a practical approximation based on the range; and algebraic estimation of the SD based on other summary statistics. Following screening of 1124 articles for methods estimating the mean, one approximate Bayesian computation approach and three papers based on alternative summary statistics were identified. Illustrative meta-analyses showed that when replacing a missing SD the approximation using the range minimised loss of precision and generally performed better than omitting trials. When estimating missing means, a formula using the median, lower quartile and upper quartile performed best in preserving the precision of the meta-analysis findings, although in some scenarios, omitting trials gave superior results. Conclusions: Methods based on summary statistics (minimum, maximum, lower quartile, upper quartile, median) reported in the literature facilitate more comprehensive inclusion of randomised controlled trials with missing mean or variability summary statistics within meta-analyses

Timing of procedural stroke and death in asymptomatic patients undergoing carotid endarterectomy::analysis of VACS, ACAS, ACST-1 and GALA RCTs

Background: The effectiveness of carotid endarterectomy (CEA) for stroke prevention depends on low procedural risks. The aim of this study was to assess the frequency and timing of procedural complications after CEA, which may clarify underlying mechanisms and help inform safe discharge policies. Methods: Individual-patient data were obtained from four large carotid intervention trials (VACS, ACAS, ACST-1 and GALA; 1983–2007). Patients undergoing CEA for asymptomatic carotid artery stenosis directly after randomization were used for the present analysis. Timing of procedural death and stroke was divided into intraoperative day 0, postoperative day 0, days 1–3 and days 4–30. Results: Some 3694 patients were included in the analysis. A total of 103 patients (2·8 per cent) had serious procedural complications (18 fatal strokes, 68 non-fatal strokes, 11 fatal myocardial infarctions and 6 deaths from other causes) [Correction added on 20 April, after first online publication: the percentage value has been corrected to 2·8]. Of the 86 strokes, 67 (78 per cent) were ipsilateral, 17 (20 per cent) were contralateral and two (2 per cent) were vertebrobasilar. Forty-five strokes (52 per cent) were ischaemic, nine (10 per cent) haemorrhagic, and stroke subtype was not determined in 32 patients (37 per cent). Half of the strokes happened on the day of CEA. Of all serious complications recorded, 44 (42·7 per cent) occurred on day 0 (20 intraoperative, 17 postoperative, 7 with unclear timing), 23 (22·3 per cent) on days 1–3 and 36 (35·0 per cent) on days 4–30. Conclusion: At least half of the procedural strokes in this study were ischaemic and ipsilateral to the treated artery. Half of all procedural complications occurred on the day of surgery, but one-third after day 3 when many patients had been discharged